If the line $ y \cos \alpha=x \sin \alpha+a \cos \alpha $ be a tangent to the circle $ x^{2}+y^{2}=a^{2} $, then

Question

If the line $ y \cos \alpha=x \sin \alpha+a \cos \alpha $ be a tangent to the circle $ x^{2}+y^{2}=a^{2} $, then, $ \sin ^{2} \alpha=1 $, $ \cos ^{2} \alpha=1 $, $ \sin ^{2} \alpha=a^{2} $, $ \cos ^{2} \alpha=a^{2} $

MARKS App · Accepted Answer

Given, y = x tan ⁡ α + a Condition for tangency is a 2 = a 2 ( 1 + tan 2 ⁡ α ) [ ∵ c 2 = a 2 ( 1 + m 2 ) ] ⇒ sec 2 ⁡ α = 1 ⇒ cos 2 ⁡ α = 1

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